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Metamath Proof Explorer

Theorem uhgrfun

Description: The edge function of an undirected hypergraph is a function. (Contributed by Alexander van der Vekens, 26-Dec-2017) (Revised by AV, 15-Dec-2020)

		Ref	Expression
	Hypothesis	uhgrfun.e	$⊢ E = iEdg (G)$
	Assertion	uhgrfun	$⊢ G \in UHGraph \to Fun E$

Proof

Step	Hyp	Ref	Expression
1		uhgrfun.e	$⊢ E = iEdg (G)$
2		eqid	$⊢ Vtx (G) = Vtx (G)$
3	2 1	uhgrf	$⊢ G \in UHGraph \to E : dom E ⟶ 𝒫 Vtx (G) ∖ \{\emptyset\}$
4	3	ffund	$⊢ G \in UHGraph \to Fun E$